Spinoza's Ethics: III.P23 - Hatred Gives Opposite

Qui id quod odio habet, tristitia affectum imaginatur, lætabitur; si contra idem lætitia affectum esse imaginetur, contristabitur et uterque hic affectus major aut minor erit prout ejus contrarius major aut minor est in eo quod odio habet.

Whoever has a thing which is with hatred, if the person imagines the thing affected with sadness, will rejoice; if, on the other hand, the person imagines the same thing to be affected with joy, will be anguished and each of these affects will be more or less the more or less it is contrary in the thing which is with hatred.

DEMONSTRATIO: Quatenus res odiosa tristitia afficitur eatenus destruitur et eo magis quo majore tristitia afficitur (per scholium propositionis 11 hujus). Qui igitur (per propositionem 20 hujus) rem quam odio habet, tristitia affici imaginatur, lætitia contra afficietur et eo majore quo majore tristitia rem odiosam affectam esse imaginatur; quod erat primum. Deinde lætitia existentiam rei lætæ ponit (per idem scholium propositionis 11 hujus) et eo magis quo major lætitia concipitur. Si quis eum quem odio habet, lætitia affectum imaginatur, hæc imaginatio (per propositionem 13 hujus) ejusdem conatum coercebit hoc est (per scholium propositionis 11 hujus) is qui odio habet, tristitia afficietur etc. Q.E.D.

Insofar as the hated thing is affected with sadness insofar as it is destroyed and the more the greater it is affected with sadness (by IIIP11S). Therefore who (by IIIP20) imagines a thing which is hated to be affected with sadness, on the other hand is affected with joy and the greater it is the more he imagines the hated thing to be affected with sadness; this was the first. Next he places with joy the existence of the joyful thing (by the same IIIP11S) and the more he conceives it the greater the joy. If anyone imagines the thing which he hates affected with joy, this imagination (by IIIP13) will restrain the person's affect, that is (by IIIP11S) who has hatred, is affected with sadness etc.

SCHOLIUM: Hæc lætitia vix solida et absque ullo animi conflictu esse potest. Nam (ut statim in propositione 27 hujus ostendam) quatenus rem sibi similem tristitiæ affectu affici imaginatur eatenus contristari debet et contra si eandem lætitia affici imaginetur. Sed hic ad solum odium attendimus.

This joy scarcely is able to be solid and away from any conflict of mind. For (as I will show shortly in IIIP27) insofar it is imagined that a thing similar to itself to be affected with an emotion of sadness just so far ought it be saddened and on the other hand if it is imagined that the same is affected with joy. But we will attend here to hatred alone.